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.\"     from: @(#)lgamma.3	6.6 (Berkeley) 12/3/92
.\"	$NetBSD: lgamma.3,v 1.22 2012/05/05 17:54:13 christos Exp $
.\"
.Dd May 4, 2012
.Dt LGAMMA 3
.Os
.Sh NAME
.Nm lgamma ,
.Nm lgammaf ,
.Nm lgamma_r ,
.Nm lgammaf_r ,
.Nm gamma ,
.Nm gammaf ,
.Nm gamma_r ,
.Nm gammaf_r ,
.Nm tgamma ,
.Nm tgammaf
.Nd log gamma function
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft extern int
.Fa signgam ;
.sp
.Ft double
.Fn lgamma "double x"
.Ft float
.Fn lgammaf "float x"
.Ft double
.Fn lgamma_r "double x" "int *sign"
.Ft float
.Fn lgammaf_r "float x" "int *sign"
.Ft double
.Fn gamma "double x"
.Ft float
.Fn gammaf "float x"
.Ft double
.Fn gamma_r "double x" "int *sign"
.Ft float
.Fn gammaf_r "float x" "int *sign"
.Ft double
.Fn tgamma "double x"
.Ft float
.Fn tgammaf "float x"
.Sh DESCRIPTION
.Fn lgamma x
.if t \{\
returns ln\||\(*G(x)| where
.Bd -unfilled -offset indent
\(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt	for x \*[Gt] 0 and
.br
\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px))	for x \*[Lt] 1.
.Ed
.\}
.if n \
returns ln\||\(*G(x)|.
.Pp
The external integer
.Fa signgam
returns the sign of \(*G(x).
.Pp
.Fn lgamma_r
is a reentrant interface that performs identically to
.Fn lgamma ,
differing in that the sign of \(*G(x) is stored in the location
pointed to by the
.Fa sign
argument and
.Fa signgam
is not modified.
.Pp
The
.Fn tgamma x
and
.Fn tgammaf x
functions return \(*G(x), with no effect on
.Fa signgam .
.Pp
.Fn gamma ,
.Fn gammaf ,
.Fn gamma_r ,
and
.Fn gammaf_r
are deprecated aliases for
.Fn lgamma ,
.Fn lgammaf ,
.Fn lgamma_r ,
and
.Fn lgammaf_r ,
respectively.
.Sh IDIOSYNCRASIES
Do not use the expression
.Dq Li signgam\(**exp(lgamma(x))
to compute g := \(*G(x).
Instead use a program like this (in C):
.Bd -literal -offset indent
lg = lgamma(x); g = signgam\(**exp(lg);
.Ed
.Pp
Only after
.Fn lgamma
has returned can signgam be correct.
.Sh RETURN VALUES
.Fn lgamma
returns appropriate values unless an argument is out of range.
Overflow will occur for sufficiently large positive values, and
non-positive integers.
For large non-integer negative values,
.Fn tgamma
will underflow.
On the
.Tn VAX ,
the reserved operator is returned,
and
.Va errno
is set to
.Er ERANGE .
.Sh SEE ALSO
.Xr math 3
.Sh HISTORY
The
.Nm lgamma
function appeared in
.Bx 4.3 .
The
.Fn tgamma
function appeared in
.Nx 6.0 .
